1. Field of the Invention
The present invention relates to an estimation apparatus for supporting estimation of a control system and estimation processing by the apparatus.
2. Description of the Related Art
The H-infinity control theory, μ synthesis theory, robust control theory, and the like are known as methods of designing a controller which controls a controlled system whose frequency characteristic varies from a manipulated variable to a controlled variable so as to make the controlled variable fall within a desired target value range.
Even with the use of the above theories, depending on required specifications such as robustness and control accuracy or the characteristics of a controlled system, a controller which satisfies all the specifications may not be available. In such a case, restrictions on required specifications are often eased to obtain a feasible controller. However, the controller obtained in this manner does not guarantee to have perfect robustness within the variation of a controlled system, and hence cannot sometimes guarantee target control accuracy with respect to the variation of the controlled system.
Demands have arisen for an estimation support apparatus for a control system, which estimates a robust control system without omission based on a designed controller within the variation range of a controlled system, checks whether stability or desired control accuracy can be obtained in the control system, and easily determines the necessity to change the design of the controller.
A control system which drives the photosensitive member of an image forming apparatus will be described as a concrete example. In an image forming apparatus including an intermediate transfer member, a developer moves from the photosensitive member surface to the intermediate transfer member surface at the contact portion between the photosensitive member and the intermediate transfer member.
In some case, in order to accurately rotate the photosensitive member or the intermediate transfer member at a predetermined rotational speed in consideration of image quality, feedback control is performed on a driving motor for the photosensitive member or the intermediate transfer member. A manipulated variable in a DC motor driving control system for the photosensitive member is a command value for motor driving, which is the duty value of a pulse width modulation (PWM) signal supplied to the motor. A controlled variable in the same control system is the rotational speed of the photosensitive member. That is, the controller computes a manipulated variable from the difference between the rotational speed of the photosensitive member detected by a sensor and a target rotational speed by proportional-integral-derivative (PID) control method, H-infinity control method, or the like.
Depending on the amount of developer or the operating environment, the photosensitive member and the intermediate transfer member slide or do not slide at the contact portion between them. That is, the transfer characteristic from a manipulated variable to a controlled variable greatly changes in the driving control system for the photosensitive member in accordance with sliding at the contact portion. When the photosensitive member and the intermediate transfer member do not slide, even if the speed of the photosensitive member is controlled, the reaction of a controlled variable to a manipulated variable is slow due to the influence of the intermediate transfer member. If they slide, the speed of the intermediate transfer member does not influence that of the photosensitive member, and the reaction of a controlled variable to a manipulated variable is quick.
In addition, in an actual operating environment, it is unknown how much sliding occurs at the contact portion. For this reason, it is necessary to construct a control system which allows the photosensitive member to stably rotate and accurately achieve a predetermined speed in any state from a state in which sliding does not occur to a state in which perfect sliding occurs (to be referred to as the state of the contact portion hereinafter). It is conceivable to use the H-infinity control theory or μ synthesis theory to design a control system requiring such robustness. However, depending on required specifications such as robustness and speed accuracy with respect to the state of the contact portion or the characteristics of the driving system such as a resonance frequency, no controller that satisfies all the specifications may be available.
For example, when using a controller which satisfies a speed accuracy specification at the sacrifice of robustness, it is necessary to estimate the behavior of rotation of the photosensitive member in the state of the contact portion which deviates from the design specifications. In contrast to this, when using a controller which satisfies the robustness requirement at the sacrifice of speed accuracy, it is necessary to estimate how much the speed accuracy requirement is not satisfied.
In these estimations, it is necessary to estimate a transfer characteristic which varies depending on the state of the contact portion without omission. If a characteristic of the driving control system for the photosensitive member matches a characteristic subjected to estimation omission, the control system may diverge, and the photosensitive member may stop rotating, rotate at a speed exceeding a target speed, or undergo large periodic speed variations.
A simulation apparatus (for example, Japanese Patent No. 3219245) is known as an estimation apparatus for the stability and control accuracy of a robust control system, which performs time-series control simulation upon formulation of a controlled system with a time-varying system transfer function, and inspects the behavior of a control system in the controlled system which varies. This apparatus can check the behavior of the robust control system without omission within the variation of the characteristic of the controlled system which can be formulated by a time-varying system.
However, the above technique can be applied only when the variation of a characteristic of a controlled system can be formulated by a time-varying transfer function. It is difficult to formulate all conditions with respect to complicated time-series variations and variations in characteristic due to individual differences between controlled systems which do not vary in a time-series manner and environments. The variation of a transfer characteristic due to the state of the contact portion in an image forming apparatus is an example of the variation of a characteristic, and hence it requires an enormous time for formulation in a controlled system having uncertainty in a frequency characteristic from a manipulated variable to a controlled variable.
As an estimation apparatus for a control system for a controlled system in which characteristic variations are difficult to formulate, MATLAB®, which is commercially available software, is known. This software performs Monte Carlo analysis upon randomly extracting characteristics from the characteristic variation range of a controlled system, and outputs a control system estimation diagram such as a Nyquist diagram for the control system. The user can determine the necessity to change the design of a controller by referring to the output results and checking the stability and control accuracy of a robust control system.
However, estimating the stability and control accuracy of the robust control system by Monte Carlo analysis may lead to estimation omission in the control system because characteristics are randomly extracted from the characteristic variation range of the controlled system.